A method of bonding two members including an aluminum alloy material as one member, and an aluminum alloy material or a pure aluminum material as the other member, the method being characterized in: that the aluminum alloy material for the one member and the aluminum alloy material for the other member are composed of an aluminum alloy containing Mg of not more than 0.5 mass %; and that a bonding process is carried out in a furnace having a non-oxidizing atmosphere at a temperature, at which a ratio of a mass of liquid phases generated in the aluminum alloy material defined as the one member to the total mass of the aluminum alloy material falls within a range from 5% to 35%, on the condition that there is either a coated fluoride-based flux or a coated chloride-based flux between both of the members to be bonded.